a 25 - foot long ladder is propped against a wall at an angle of 18° with the wall. how high up the wall…

a 25 - foot long ladder is propped against a wall at an angle of 18° with the wall. how high up the wall does the ladder reach? round the answer to the nearest tenth of a foot.\n13.8 ft\n23.8 ft\n26.3 ft\n80.9 ft

a 25 - foot long ladder is propped against a wall at an angle of 18° with the wall. how high up the wall does the ladder reach? round the answer to the nearest tenth of a foot.\n13.8 ft\n23.8 ft\n26.3 ft\n80.9 ft

Answer

Explanation:

Step1: Identify the trig - relation

We have a right - triangle where the length of the ladder is the hypotenuse ($c = 25$ feet) and we want to find the adjacent side ($x$) to the given angle $\theta=18^{\circ}$ with respect to the wall. We use the cosine function: $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. $\cos\theta=\frac{x}{c}$

Step2: Substitute the values

Substitute $\theta = 18^{\circ}$ and $c = 25$ into the formula. $x = c\times\cos\theta=25\times\cos(18^{\circ})$ Since $\cos(18^{\circ})\approx0.9511$, then $x = 25\times0.9511 = 23.7775$

Step3: Round the answer

Round $23.7775$ to the nearest tenth. $x\approx23.8$

Answer:

23.8 ft